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Unformatted text preview: and a force due to air resistence, which can be accurately modeled as proportional to the velocity v of the object, saybv for some constant b > . Here, g is the constant acceleration of gravity near the earth’s surface. By Newton’s second law, the force should be equal to the mass of the object times its acceleration dv dt . a) Show that the function v ( t ) = mg b ± 1ebt/m ² satisﬁes m dv dt = mgbv for all t . b) Calculate lim t →∞ v ( t ) . What does it imply about the velocity of the object as time passes? c) For any ﬁxed (constant) time t , calculate lim b → + v ( b ) . What does it imply about an object falling without air resistence?...
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 Spring '08
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 Calculus, Derivative, Limits, Mass, General Relativity, Limit of a function

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